Housings of exhaust gas-treating device, for example, catalytic converters and particle filters, usually have a jacket closed in the circumferential direction for mounting at least one exhaust gas-treating element. This jacket may pass over at least at one axial end into a ring body, which is closed in the circumferential direction and is, for example, funnel-shaped, with which the housing can be connected to another component of the exhaust system. Furthermore, it is common practice to manufacture the jacket by rolling from a steel sheet billet, whereas the corresponding ring body is preferably manufactured by deep-drawing. The rolled jacket, which is welded at its abutting edges, is then axially connected to the ring body, namely, preferably by means of a weld seam. This conventional procedure for manufacturing such a housing is associated with a comparatively great effort.